223 Answered Questions for the topic Limits

12/13/17

I have a question regarding limits
Find the limit as x goes to 0:   (ln(1+x2)-x(arctan(x)))/(x(sin(x)-x))     At first the fraction found is 0/0, but applying L'Hopitals rule, when differentiated the answer is again 0/0,  and... more
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12/12/17

As x approaches 0 x / (sin3x)
To solve a limit as x is approaching 0 while the function is x / (sin3x), what is the step by step process...? I've seen many sites online that go through this problem, yet is completely confusing... more
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Limits

11/21/17

find the limit without using L'Hospital's rule
lim x->-pi/2 (1+ cos (2x))/(2x+ pi )^2
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Limits

11/20/17

Prove by using the formal definition of limit that limx--->∞ 1/(x^4+x^2+5)=0
This is what I have so far:   Limx-->∞ 1/(x^4+x^2+5)=0 if for all ϵ>0 we find a value x_c depending on ϵ such that | 1/(x^4+x^2+5)|< ϵ   I dont know what to do afterwards
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11/13/17

Determine whether the sequence converges or diverges. If it converges find the limit.
an=e(-1/sqrt(n)) Apparently in converges and the limit is 1 but I'm not really sure how to do this type of problem with a limit of ex   {n2e-n} Limit converges to 0? How?    
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Limits Calculus 1

11/08/17

Find the limit as x approaches pi/2 from the left of
(tanx/7)/(2x-pi)
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Limits

10/25/17

Why is the limit as n=>0+ of this = -1?
So the limit as n=> 0+ for abs(X^2 - x/100)/(x^2 - x/100) = -1, NOT 1, as I initially thought.    My logic in getting 1 was that plugging in small integral values > 0 (since it's... more
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Limits Math

10/14/17

Find multivariable limits
Find multivariable limits and explain   lim (x,y) -> (0,0) = (x^4-y^4)/(x^2+y^2)   lim (x,y) -> (0,0) = xy/sqrt(x^2+y^2)
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Limits True Or False

10/12/17

True or False: limits
a) if limit of f(x) as x approaches a exists, then limit of  |f(x)| as x approaches a exists.  is this true or false? why or why not?   b) if limit of |f(x)| as x approaches a exists, then limit... more
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Limits Asymptotes Sine

10/08/17

horizontal and vertical asymptotes of y=x/sinx
find all horizontal and vertical asymptotes of  y=x/sinx   vertical asymptotes: if i set denominator to 0, then sinx=0 and x= 0 or npi?    horizontal asymptotes: i have to find the limit of... more
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10/08/17

if limit of f(x) as x approaches a exists, does the limit of |f(x)|exist as as x approaches a? vice versa?
a) If lim f(x) exists, them lim |f(x)| exists        x>a                         x>a   b) if lim |f(x)| exists, then lim f(x) exists         x>a                         ... more
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Limits Calculus Lim

10/04/17

Use the formal definition of limit to prove that lim x-->2(1-4x)=-7
With steps please  using the epsilom-delta definition
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10/01/17

Let {xn} be a bounded sequence such that any of its convergent proper subsequences converge to the same limit l. Prove that {xn} converges to l.
Any hints on how to prove this? What can we use a a proper subsequence, knowing that a proper subsequence is any subsequence except for the sequence it self. 
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Limits Calculus 1

09/21/17

I need help finding the limit/showing that it doesn't exist (Calc 1)
limx-->infinity (square root(9x2+x) - 3x)
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Limits

09/05/17

I don't understand how cos^2(theta)-1 = -sin^2(theta)
Could someone explain
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Limits

09/02/17

lim x->c- (c^2-x^2)/(|x-c|) e. Evaluate the limits or explain why it does not exist
lim        (c^2-x^2)/(|x-c|) x->c- e. Evaluate the limits or explain why it does not exist
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Limits

08/31/17

Find the limit
if f(x)= x^3-4 then find limit h→0 f(x+h)-f(x)/h
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Limits

08/31/17

Find the constant C
lim x→2 x^2+x+C/ x^2-3x+2 so that the limit exists 
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08/31/17

Using the squeeze theorem: lim x--> 0+ (e^x -1) * 3^(2cos(π/x))
lim x->0+   (ex-1) * 32cos(π/x)
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08/29/17

solve the limit using the binomial theorem: lim x --> 0 (5x-2)^3+8 / (2x+3)^3 -27
 solve the limit using the binomial theorem:   lim        (5x-2)^3+8 / (2x+3)^3 -27 x --> 0
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08/26/17

Is there a number to "a" such that the limit exists? If so, find the value of "a" and find the limit. If not, explain why.
Find the limit as "x" approaches 3 F(x)= (2x2-3ax+x-a-1)/ x2-2x-3 **I already know that if you substitute in 3 for x, the denominator will be 0 and therefore it cannot exist. I'm wondering if... more
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07/25/17

lim (x,y)->(0,0) of (y-sin(y))/(x^2+y^2)
I have this function for (x,y)=(0,0) f=0 and on the other f=(y-sin(y))/(x^2+y^2) is lim (x,y)->(0,0) of (y-sin(y))/(x^2+y^2) = 0 ? according to wolfarm no but can someone show me why?
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07/22/17

Indeterminate Forms and L'Hospital's Rule
Find the limit as x approaches 1 from the right    x^(1/(x-1))
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Limits Math Calculus

07/20/17

Calculus Question
Evaluate the following limit:   sinx/tanx as x approaches 0.   Help?!
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Limits Math Calculus

07/20/17

Calculus Question
Evaluate the following limit:   lim of sin(4theta)/(5theta) as theta approaches 0.   Help!?
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